DTI (debt to income) at origination is not a strong predictor of default.

What really matters in the default decision is the mortgage payment relative to the borrower’s income in the present and future, not the borrower’s income in the past. Consequently, the high degree of volatility in individual incomes means that mortgages that start out with low DTIs can end in default if housing prices are falling.

The evidence that a foreclosure loses money for the lender seems compelling. The servicer typically resells a foreclosed house for much less than the outstanding balance on the mortgage ... This would seem to imply that the ultimate owners of a securitized mortgage, the investors, lose money when a foreclosure occurs. Estimates of the total gains to investors from modifying rather than foreclosing can run to $180 billion, more than 1 percent of GDP. It is natural to wonder why investors are leaving so many $500 bills on the sidewalk. While contract frictions are one possible explanation, another is that the gains from loan modifications are in reality much smaller or even nonexistent from the investor’s point of view.

We provide evidence in favor of the latter explanation. First, the typical calculation purporting to show that an investor loses money when a foreclosure occurs does not capture all relevant aspects of the problem. Investors also lose money when they modify mortgages for borrowers who would have repaid anyway, especially if modifications are done en masse, as proponents insist they should be. Moreover, the calculation ignores the possibility that borrowers with modified loans will default again later, usually for the same reason they defaulted in the first place. These two problems are empirically meaningful and can easily explain why servicers eschew modification in favor of foreclosure.emphasis added

This analysis suggests mortgage modifications - without principal reduction - will have limited success. The authors suggest that loan or grants to homeowners with lost income might be more effective than mortgage modifications.

The authors also makes several other important points:

On "walking away" or "ruthless default" (when the borrower walks away because they refuse to make payments on an underwater house).

If there is no hope that the price of the house will ever recover to exceed the outstanding balance on the mortgage, the borrower may engage in “ruthless default” and simply walk away from the home. Kau, Keenan, and Kim (1994) show that optimal ruthless default takes place at a negative-equity threshold that is well below zero, due to the option value of waiting to see whether the house price recovers.

But the authors conclude that ruthless defaults are only a small part of the current foreclosure problem:

To sum up, falling house prices are no doubt causing some people to ruthlessly default. But the data indicate that ruthless defaults are not the biggest part of the foreclosure problem. For the nation as a whole, less than 40 percent of homeowners who had their first 90-day delinquency in 2008 stopped making payments abruptly. Because this figure is an upper bound on the fraction of ruthless defaults, it suggests ruthless default is not the main reason why falling house prices have caused so many foreclosures.

Negative equity is key to defaults (Falling house prices!)

The empirical evidence on the role of negative equity in causing foreclosures is overwhelming and incontrovertible. Household-level studies show that the foreclosure hazard for homeowners with positive equity is extremely small but rises rapidly as equity approaches and falls below zero.

Many commentators have put the resets at the heart of the crisis, but the simulations illustrate that it is difficult to support this claim. The payment escalation story is relevant if we assume that there is no income risk and that the initial DTI is also the threshold for ex post DTI. Then loans with resets become unaffordable 100 percent of the time and loans without resets never become unaffordable. But adding income risk essentially ruins this story. If the initial DTI is also the threshold for ex post DTI, then, with income risk, about 70 percent of the loans will become unaffordable even without the reset. The reset only raises that figure to about 80 percent. If, on the other hand, we set the ex post affordability threshold well above the initial DTI, then the resets are not large enough to cause ex post affordability problems.

These are all key points.

I think it is important to understand that loans with high DTI were an enabler for speculation during the housing bubble, and this speculation pushed up house prices. So, although the authors argue high initial DTI loans are not a good predictor of defaults, the prevalence of high DTI loans was evidence of a bubble - and a good predictor of a housing bust.